A Fast Algorithm for the BDS Statistic

The BDS statistic has proved to be one of several useful nonlinear diagnostics. It has been shown to have good power against many nonlinear alternatives, and its asymptotic properties as a residual diagnostic are well understood. Furthermore, extensive Monte Carlo results have proved it useful in relatively small samples. However, the BDS test is not trivial to calculate, and is even more difficult to deal with if one wants the speed necessary to make bootstrap resampling feasible. This short paper presents a fast algorithm for the BDS statistic, and outlines how these speed improvements are achieved. Source code in the C programming language is included.